<s>
Binary	B-Device
offset	I-Device
carrier	I-Device
modulation	I-Device
(	O
BOC	O
modulation	B-Application
)	O
was	O
developed	O
by	O
John	O
Betz	O
in	O
order	O
to	O
allow	O
interoperability	O
of	O
satellite	O
navigation	O
systems	O
.	O
</s>
<s>
It	O
is	O
currently	O
used	O
in	O
the	O
US	O
GPS	O
system	O
,	O
Indian	O
IRNSS	O
system	O
and	O
in	O
Galileo	O
and	O
is	O
a	O
square	O
sub-carrier	O
modulation	B-Application
,	O
where	O
a	O
signal	O
is	O
multiplied	O
by	O
a	O
rectangular	O
sub-carrier	O
of	O
frequency	O
equal	O
to	O
or	O
greater	O
than	O
the	O
chip	O
rate	O
.	O
</s>
<s>
Following	O
this	O
sub-carrier	O
multiplication	O
,	O
the	O
spectrum	O
of	O
the	O
signal	O
is	O
divided	O
into	O
two	O
parts	O
,	O
therefore	O
BOC	O
modulation	B-Application
is	O
also	O
known	O
as	O
a	O
split-spectrum	O
modulation	B-Application
.	O
</s>
<s>
The	O
main	O
idea	O
behind	O
BOC	O
modulation	B-Application
is	O
to	O
reduce	O
the	O
interference	O
with	O
BPSK-modulated	O
signal	O
,	O
which	O
has	O
a	O
sinc	B-Algorithm
function	I-Algorithm
shaped	O
spectrum	O
.	O
</s>
<s>
Therefore	O
,	O
BPSK-modulated	O
signals	O
such	O
as	O
C/A	O
GPS	O
codes	O
have	O
most	O
of	O
their	O
spectral	O
energy	O
concentrated	O
around	O
the	O
carrier	O
frequency	O
,	O
while	O
BOC-modulated	O
signals	O
(	O
used	O
in	O
Galileo	O
system	O
)	O
have	O
low	O
energy	O
around	O
the	O
carrier	O
frequency	O
and	O
two	O
main	O
spectral	O
lobes	O
further	O
away	O
from	O
the	O
carrier	O
(	O
thus	O
,	O
the	O
name	O
of	O
split-spectrum	O
)	O
.	O
</s>
<s>
BOC	O
modulation	B-Application
has	O
several	O
variants	O
:	O
sine	O
BOC	O
(	O
sinBOC	O
)	O
,	O
cosine	O
BOC	O
(	O
cosBOC	O
)	O
,	O
alternative	O
BOC	O
(	O
altBOC	O
)	O
,	O
multiplexed	B-Device
BOC	I-Device
(	O
MBOC	B-Device
)	O
,	O
double	O
BOC	O
(	O
DBOC	O
)	O
etc	O
.	O
</s>
<s>
A	O
sine	O
BOC(1, 1 )	O
modulation	B-Application
is	O
similar	O
to	O
Manchester	B-Protocol
code	I-Protocol
,	O
that	O
is	O
,	O
in	O
digital	O
domain	O
,	O
a	O
'	O
+1	O
 '	O
is	O
encoded	O
as	O
a	O
'	O
+1	O
−1	O
 '	O
sequence	O
,	O
and	O
a	O
'	O
0	O
 '	O
is	O
encoded	O
as	O
a	O
'	O
−1	O
+1	O
 '	O
sequence	O
.	O
</s>
<s>
For	O
an	O
arbitrary	O
modulation	B-Application
order	O
,	O
in	O
sine	O
BOC(m, n )	O
case	O
,	O
a	O
'	O
+1	O
 '	O
is	O
encoded	O
as	O
an	O
alternating	O
sequence	O
of	O
'	O
+1	O
−1	O
+1	O
−1	O
+1	O
...	O
'	O
,	O
having	O
elements	O
,	O
and	O
a	O
'	O
0	O
 '	O
(	O
or	O
'	O
−1	O
 '	O
)	O
is	O
encoded	O
as	O
an	O
alternating	O
'	O
−1	O
+1	O
...	O
'	O
sequence	O
,	O
also	O
having	O
elements	O
.	O
</s>
<s>
BOC	O
modulation	B-Application
is	O
typically	O
applied	O
on	O
CDMA	B-Protocol
signals	O
,	O
where	O
each	O
chip	O
of	O
the	O
pseudorandom	B-Error_Name
code	O
is	O
split	O
into	O
BOC	O
sub-intervals	O
,	O
as	O
explained	O
above	O
(	O
i.e.	O
,	O
there	O
are	O
BOC	O
intervals	O
per	O
chip	O
)	O
.	O
</s>
<s>
The	O
power	B-Algorithm
spectral	I-Algorithm
density	I-Algorithm
of	O
a	O
BOC-modulated	O
signal	O
depends	O
on	O
the	O
BOC	O
modulation	B-Application
order	O
.	O
</s>
<s>
BOC-modulated	O
signals	O
,	O
by	O
difference	O
with	O
BPSK	O
signals	O
,	O
create	O
the	O
so-called	O
ambiguities	O
in	O
the	O
correlation	O
function	O
.	O
</s>
<s>
The	O
BOC-modulated	O
signals	O
in	O
GNSS	O
can	O
be	O
processed	O
either	O
with	O
a	O
Full	O
BOC	O
receiver	O
or	O
via	O
various	O
unambiguous	O
approaches	O
.	O
</s>
